What are the benefits of the new torment levels?

Even assuming that you want to exclusively run greater rifts, the new torment levels will help you continue to do so. Greater rifts require GR keys that drop from normal Nephalem rift bosses. At higher torment levels, these bosses will drop multiple keys. This table shows how many keys you can get at various difficulty levels, with fractional units being the percentage chance of receiving an additional key.

| Difficulty | T1  |  T6  | T10 | T11 | T13  | T14  | T15 | T16  |
| Keys/rift  | 1.2 | 1.51 | 1.9 |  2  | 2.25 | 2.66 |  3  | 3.25 |

More keys per Nephalem rift means fewer low-experience rifts and more time doing greater rifts. The linked resource also points out the other benefits of the higher difficulty levels including a higher legendary drop rate, more gold, more death's breaths, and more Horadric cache materials.

The new torment levels allow content that does not use the Greater Rift levels to be at a higher level. Think of for example the non existing secret cow level. Or for example the Vault which are created in your current world at the difficulty that the game is in. As each torment level increases gold drop, chance for legendaries, etc these zones gain the benefit of the bonuses these new torment levels bring.